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From Wikipedia, the free encyclopedia
(Redirected from Hexidecimal)
In mathematics and computer science, hexadecimal (also
base 16, or hex) is a positional numeral system with a
radix, or base, of 16. It uses sixteen distinct symbols, most
often the symbols 0–9 to represent values zero to nine, and
A, B, C, D, E, F (or alternatively a through f) to represent
values ten to fifteen. For example, the hexadecimal number
2AF3 is equal, in decimal, to (2 × 163) + (10 × 162) + (15 ×
161) + (3 × 160) , or 10,995.
Each hexadecimal digit represents four binary digits (bits)
(also called a "nibble"), and the primary use of
hexadecimal notation is as a human-friendly representation
of binary coded values in computing and digital electronics.
For example, byte values can range from 0 to 255 (decimal)
but may be more conveniently represented as two
hexadecimal digits in the range 00 through FF.
Hexadecimal is also commonly used to represent computer
memory addresses.
1 Representing hexadecimal
2 Verbal and digital representations
3 Signs
4 Binary conversion
5 Converting from other bases
5.1 Division-remainder in source base
5.2 Addition and multiplication
5.3 Tools for conversion
Numeral systems by culture
Hindu-Arabic numerals
Western Arabic Khmer
Eastern Arabic Mongolian
Indian family
Thai
Burmese
East Asian numerals
Chinese
Korean
Japanese
Vietnamese
Suzhou
Counting rods
Alphabetic numerals
Abjad
Ge'ez
Armenian
Greek (Ionian)
Hebrew
Āryabhaṭa
Cyrillic
Other systems
Aegean
Inuit
Attic
Mayan
Babylonian
Quipu
Brahmi
Roman
Egyptian
Sumerian
Etruscan
Urnfield
List of numeral system topics
Positional systems by base
Decimal (10)
1, 2, 3, 4, 5, 8, 12, 16, 20, 60
more…
6 Real numbers
6.1 Powers
7 Cultural
7.1 Etymology
7.2 Common patterns and humor
7.3 Primary numeral system
8 Key to number base notation
9 See also
10 References
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In situations where there is no context, a hexadecimal
number might be ambiguous and confused with numbers
expressed in other bases. There are several conventions for
expressing values unambiguously. A numerical subscript
(itself written in decimal) can give the base explicitly: 15910 is
decimal 159; 15916 is hexadecimal 159, which is equal to
34510. Other authors prefer a text subscript, such as
159decimal and 159hex, or 159d and 159h.
In linear text systems, such as those used in most computer
programming environments, a variety of methods have arisen:
0hex
1hex
2hex
3hex
=
=
=
=
0dec
1dec
2dec
3dec
=
=
=
=
0oct
1oct
2oct
3oct
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
4hex
5hex
6hex
7hex
=
=
=
=
4dec
5dec
6dec
7dec
=
=
=
=
4oct
5oct
6oct
7oct
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
8hex
9hex
Ahex
Bhex
= 8dec =
= 9dec =
= 10dec =
= 11dec =
10oct
11oct
12oct
13oct
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
In URLs, character codes are written as hexadecimal
pairs prefixed with %: http://www.example.com
/name%20with%20spaces where %20 is the space
(blank) character (code value 20 in hex, 32 in decimal).
Chex = 12dec = 14oct 1 1 0 0
In XML and XHTML, characters can be expressed as
hexadecimal numeric character references using the
Dhex = 13dec = 15oct 1 1 0 1
notation &#xcode;, where code is the 1- to 6-digit hex
Ehex = 14dec = 16oct 1 1 1 0
number assigned to the character in the Unicode
Fhex = 15dec = 17oct 1 1 1 1
standard. Thus ’ represents the curled right
single quote (Unicode value 2019 in hex, 8217 in decimal).
Color references in HTML and CSS can be expressed with six hexdigits (two each for the
red, green, and blue components, in that order) prefixed with #: white, for example, is
represented #FFFFFF .[1] CSS allows 3-hexdigit abbreviations with one hexdigit per
component: #FA3 abbreviates #FFAA33 (a golden orange).
*nix (Unix and related) shells, and likewise the C programming language, which was
designed for Unix (and the syntactic descendants of C[2]) use the prefix 0x for numeric
constants represented in hex: 0x5A3. Character and string constants may express
character codes in hexadecimal with the prefix \x followed by two hex digits: '\x1B'
represents the Esc control character; "\x1B[0m\x1B[25;1H" is a string containing 11
characters (plus a trailing NUL to mark the end of the string) with two embedded Esc
characters.[3] To output an integer as hexadecimal with the printf function family, the format
conversion code %X or %x is used.
In the Unicode standard, a character value is represented with U+ followed by the hex
value: U+20AC is the Euro sign (€).
In MIME (e-mail extensions) quoted-printable encoding, characters that cannot be
represented as literal ASCII characters are represented by their codes as two hexadecimal
digits (in ASCII) prefixed by an equal to sign =, as in Espa=F1a to send "España" (Spain).
(Hexadecimal F1, equal to decimal 241, is the code number for the lower case n with tilde in
the ISO/IEC 8859-1 character set.)
In Intel-derived assembly languages, hexadecimal is indicated with a suffixed H or h: FFh or
05A3H. Some implementations require a leading zero when the first hexadecimal digit
character is not a decimal digit: 0FFh
Other assembly languages (6502, AT&T, Motorola), Pascal, Delphi, some versions of BASIC
(Commodore) and Forth use $ as a prefix: $5A3.
Some assembly languages (Microchip) use the notation H'ABCD' (for ABCD16).
Ada and VHDL enclose hexadecimal numerals in based "numeric quotes": 16#5A3#. VHDL
also supports x"5A3".
Verilog represents hexadecimal constants in the form 8'hFF, where 8 is the number of bits
in the value and FF is the hexadecimal constant.
Modula-2 and some other languages use # as a prefix: #05A3
The Smalltalk programming language uses the prefix 16r: 16r5A3
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Postscript indicates hex with prefix 16#: 16#5A3. Binary data (such as image pixels) can be
expressed as unprefixed consecutive hexadecimal pairs: AA213FD51B3801043FBC...
In early systems when a Macintosh crashed, one or two lines of hexadecimal code would be
displayed under the Sad Mac to tell the user what went wrong.
Common Lisp use the prefixes #x and #16r.
MSX BASIC[4], QuickBASIC, FreeBASIC and Visual Basic prefix hexadecimal numbers with
&H: &H5A3
BBC BASIC and Locomotive BASIC use & for hex.[5]
TI-89 and 92 series uses a 0h prefix: 0h5A3
Notations such as X'5A3' are sometimes seen, such as in PL/I. This is the most common
format for hexadecimal on IBM mainframes (zSeries) and midrange computers (iSeries)
running traditional OS's (zOS, zVSE, zVM, TPF, OS/400), and is used in Assembler, PL/1,
Cobol, JCL, scripts, commands and other places. This format was common on other (and
now obsolete) IBM systems as well.
Donald Knuth introduced the use of a particular typeface to represent a particular radix in
his book The TeXbook.[6] Hexadecimal representations are written there in a typewriter
typeface: 5A3
Any IPv6 address can be written as eight groups of four hexadecimal digits, where each
group is separated by a colon (:). This, for example, is a valid IPv6 address:
2001:0db8:85a3:0000:0000:8a2e:0370:7334
There is no universal convention to use lowercase or
uppercase for the letter digits, and each is prevalent or
preferred in particular environments by community standards
or convention.
The choice of the letters A through F to represent the digits
above nine was not universal in the early history of computers.
During the 1950s, some installations favored using the digits 0
through 5 with a macron character ("¯") to indicate the values
Bruce A. Martin's hexadecimal
10–15. Users of Bendix G-15 computers used the letters U
notation proposal
through Z. Bruce A. Martin of Brookhaven National Laboratory
considered the choice of A–F "ridiculous" and in a 1968 letter
to the editor of the CACM proposed an entirely new set of symbols based on the bit locations,
which did not gain much acceptance.[7]
There are no traditional numerals to represent the quantities from ten to fifteen—letters are used
as a substitute—and most Western European languages lack non-decimal names for the
numerals above ten. Even though English has names for several non-decimal powers (pair for
the first binary power, score for the first vigesimal power, dozen, gross, and great gross for the
first three duodecimal powers), no English name describes the hexadecimal powers (decimal 16,
256, 4096, 65536, ... ). Some people read hexadecimal numbers digit by digit like a phone
number: 4DA is "four-dee-ay". However, the letter A sounds like "eight", C sounds like "three",
and D can easily be mistaken for the "-ty" suffix: Is it 4D or forty? Other people avoid confusion by
using the NATO phonetic alphabet: 4DA is "four-delta-alfa"; or the Joint Army/Navy Phonetic
Alphabet ("four-dog-able"); or a similar ad hoc system.
Systems of counting on digits have been devised for both binary and hexadecimal. Arthur C.
Clarke suggested using each finger as an on/off bit, allowing finger counting from zero to 1023
on ten fingers. Another system for counting up to FF (255) is illustrated on the right; it seems to
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be an extension of an existing system for counting in twelves
(dozens and grosses), that is common in South Asia and
elsewhere.
The hexadecimal system can express negative numbers the
same way as in decimal: –2A to represent –42 and so on.
However, some prefer instead to express the exact bit patterns
Hexadecimal finger-counting
used in the processor and consider hexadecimal values best
scheme.
handled as signed values. This way, the negative number –42
can be written as FFFF FFD6 in a 32-bit CPU register, as
C228 0000 in a 32-bit FPU register or C045 0000 0000 0000 in a 64-bit FPU register (assuming
certain representation schemes, two's-complement in the 32-bit non-FPU instance and
sign-magnitude in the FPU instances.)
Most computers manipulate binary data, but it is difficult for humans to work with the large
number of digits for even a relatively small binary number. Although most humans are familiar
with the base 10 system, it is much easier to map binary to hexadecimal than to decimal because
each hexadecimal digit maps to a whole number of bits (410). This example converts 11112 to
base ten. Since each position in a binary numeral can contain either a 1 or 0, its value may be
easily determined by its position from the right:
00012 = 110
00102 = 210
01002 = 410
10002 = 810
Therefore:
11112 = 810 + 410 + 210 + 110
= 1510
With surprisingly little practice, mapping 11112 to F16 in one step becomes easy: see table in
Representing hexadecimal. The advantage of using hexadecimal rather than decimal increases
rapidly with the size of the number. When the number becomes large, conversion to decimal is
very tedious. However, when mapping to hexadecimal, it is trivial to regard the binary string as
4-digit groups and map each to a single hexadecimal digit.
This example shows the conversion of a binary number to decimal, mapping each digit to the
decimal value, and adding the results.
010111101011010100102
= 26214410 + 6553610 + 3276810 + 1638410 + 819210 + 204810 + 51210
+ 25610 + 6410 + 1610 + 210
= 38792210
Compare this to the conversion to hexadecimal, where each group of four digits can be
considered independently, and converted directly:
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010111101011010100102 = 0101 1110 1011 0101 00102
= 5
E
B
5
216
= 5EB5216
The conversion from hexadecimal to binary is equally direct.
The octal system can also be useful as a tool for people who need to deal directly with binary
computer data. Octal represents data as three bits per character, rather than four.
Division-remainder in source base
As with all bases there is a simple algorithm for converting a representation of a number to
hexadecimal by doing integer division and remainder operations in the source base. Theoretically
this is possible from any base but for most humans only decimal and for most computers only
binary (which can be converted by far more efficient methods) can be easily handled with this
method.
Let d be the number to represent in hexadecimal, and the series hihi-1...h2h1 be the hexadecimal
digits representing the number.
1.
2.
3.
4.
i := 1
hi := d mod 16
d := (d-hi) / 16
If d = 0 (return series hi) else increment i and go to step 2
"16" may be replaced with any other base that may be desired.
The following is a JavaScript implementation of the above algorithm for converting any number to
a hexadecimal in String representation. Its purpose is to illustrate the above algorithm. To work
with data seriously however, it is much more advisable to work with bitwise operators.
function toHex(d) {
var r = d % 16;
var result;
if (d-r == 0)
result = toChar(r);
else
result = toHex( (d-r)/16 ) + toChar(r);
return result;
}
function toChar(n) {
const alpha = "0123456789ABCDEF";
return alpha.charAt(n);
}
Addition and multiplication
It is also possible to make the conversion by assigning each place in the source base the
hexadecimal representation of its place value and then performing multiplication and addition to
get the final representation. I.e. to convert the number B3AD to decimal one can split the
conversion into D (1310), A (1010), 3 (310) and B (1110) then get the final result by multiplying
each decimal representation by 16p, where 'p' is the corresponding position from right to left,
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beginning with 0. In this case we have 13*(160) + 10*(161) +
3*(162) + 11*(163), which is equal 45997 in the decimal
system.
Tools for conversion
Most modern computer systems with graphical user interfaces
provide a built-in calculator utility, capable of performing
conversions between various radixes, generally including
hexadecimal.
In Microsoft Windows, the Calculator utility can be set to
A hexadecimal multiplication
Scientific mode (called Programmer mode in some versions),
table
which allows conversions between radix 16 (hexadecimal), 10
(decimal), 8 (octal) and 2 (binary); the bases most commonly
used by programmers. In Scientific Mode, the on-screen numeric keypad includes the
hexadecimal digits A through F which are active when "Hex" is selected. In hex mode, however,
the Windows Calculator only supports integers.
As with other numeral systems, the hexadecimal system can be used to represent rational
numbers, although recurring digits are common since sixteen (10h) has only a single prime factor
(two):
½ = 0.8
⅙ = 0.2A
⅓ = 0.5
1⁄7 = 0.249
¼ = 0.4
⅕ = 0.3
⅛ = 0.2
1⁄9 = 0.1C7
1⁄A = 0.19
1⁄E = 0.1249
1⁄B = 0.1745D
1⁄F = 0.1
1⁄C = 0.15
1⁄10 = 0.1
1⁄D = 0.13B
1⁄11 = 0.0F
where an overline indicates a recurring pattern.
For any base, 0.1 (or "1/10") is always equivalent to one divided by the representation of that
base value in its own number system: Counting in base 3 is 0, 1, 2, 10 (three). Thus, whether
dividing one by two for binary or dividing one by sixteen for hexadecimal, both of these fractions
are written as 0.1. Because the radix 16 is a perfect square (4²), fractions expressed in
hexadecimal have an odd period much more often than decimal ones, and there are no cyclic
numbers (other than trivial single digits). Recurring digits are exhibited when the denominator in
lowest terms has a prime factor not found in the radix; thus, when using hexadecimal notation, all
fractions with denominators that are not a power of two result in an infinite string of recurring
digits (such as thirds and fifths). This makes hexadecimal (and binary) less convenient than
decimal for representing rational numbers since a larger proportion lie outside its range of finite
representation.
All rational numbers finitely representable in hexadecimal are also finitely representable in
decimal, duodecimal and sexagesimal: that is, any hexadecimal number with a finite number of
digits has a finite number of digits when expressed in those other bases. Conversely, only a
fraction of those finitely representable in the latter bases are finitely representable in
hexadecimal. For example, decimal 0.1 corresponds to the infinite recurring representation
0.199999999999... in hexadecimal. However, hexadecimal is more efficient than bases 12 and 60
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for representing fractions with powers of two in the denominator (e.g., decimal one sixteenth is
0.1 in hexadecimal, 0.09 in duodecimal, 0;3,45 in sexagesimal and 0.0625 in decimal).
In decimal
In hexadecimal
Prime factors of the base: 2, 5
Prime factors of the base: 2
Prime
factors
Fraction
of the
denominator
Positional representation
Positional
representation
Prime
factors
Fraction
of the
denominator
1/2
2
0.5
0.8
2
1/2
1/3
3
0.3333... = 0.3
0.5555... = 0.5
3
1/3
1/4
2
0.25
0.4
2
1/4
1/5
5
0.2
0.3
5
1/5
1/6
2, 3
0.16
0.2A
2, 3
1/6
1/7
7
0.142857
0.249
7
1/7
1/8
2
0.125
0.2
2
1/8
1/9
3
0.1
0.1C7
3
1/9
1/10
2, 5
0.1
0.19
2, 5
1/A
1/11
11
0.09
0.1745D
B
1/B
1/12
2, 3
0.083
0.15
2, 3
1/C
1/13
13
0.076923
0.13B
D
1/D
1/14
2, 7
0.0714285
0.1249
2, 7
1/E
1/15
3, 5
0.06
0.1
3, 5
1/F
1/16
2
0.0625
0.1
2
1/10
1/17
17
0.0588235294117647
0.0F
11
1/11
1/18
2, 3
0.05
0.0E38
2, 3
1/12
1/19
19
0.052631578947368421
0.0D79435E50
13
1/13
1/20
2, 5
0.05
0.0C
2, 5
1/14
1/21
3, 7
0.047619
0.0C3
3, 7
1/15
1/22
2, 11
0.045
0.0BA2E8
2, B
1/16
1/23
23
0.0434782608695652173913
0.0B21642C8590
17
1/17
1/24
2, 3
0.0416
0.0A
2, 3
1/18
1/25
5
0.04
0.0A3D70
5
1/19
1/26
2, 13
0.0384615
0.09D8
2, B
1/1A
1/27
3
0.037
0.097B425ED
3
1/1B
1/28
2, 7
0.03571428
0.0924
2, 7
1/1C
1/29
29
0.0344827586206896551724137931 0.08D3DCB
1D
1/1D
1/30
2, 3, 5
2, 3, 5
1/1E
1/31
1F
1/1F
1/32
2
1/20
0.03
0.08
31
0.032258064516129
0.08421
2
0.03125
0.08
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1/33
3, 11
0.03
0.07C1F
3, B
1/21
1/34
2, 17
0.02941176470588235
0.078
2, 11
1/22
1/35
5, 7
0.0285714
0.075
5, 7
1/23
1/36
2, 3
0.027
0.071C
2, 3
1/24
Algebraic irrational
number
In decimal
√2 (the length of the diagonal 1.41421356237309...
of a unit square)
√3 (the length of the diagonal
of a unit cube)
1.73205080756887...
√5 (the length of the diagonal 2.2360679774997...
of a 1×2 rectangle)
φ (phi, the golden ratio =
(1+√5)⁄2)
1.6180339887498...
In hexadecimal
1.6A09E667F3BCD...
1.BB67AE8584CAA...
2.3C6EF372FE95...
1.9E3779B97F4A...
Transcendental irrational
number
π (pi, the ratio of circumference 3.1415926535897932384626433 3.243F6A8885A308D313198A2E0
8327950288419716939937510... 3707344A4093822299F31D008...
to diameter)
e (the base of the natural
logarithm)
τ (the Thue–Morse constant)
2.7182818284590452...
2.B7E151628AED2A6B...
0.412454033640...
0.6996 9669 9669 6996 ...
0.5772156649015328606...
0.93C467E37DB0C7A4D1B...
Number
γ (the limiting difference
between the harmonic series
and the natural logarithm)
Powers
Possibly the most widely used powers, powers of two, are easier to show using base 16. The first
sixteen powers of two are shown below.
2x
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value
20
1
21
2
22
4
23
8
24
10hex
25
20hex
26
40hex
27
80hex
28
100hex
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200hex
2A (
) 400hex
2B (
) 800hex
2C (
) 1000hex
2D (
) 2000hex
2E (
) 4000hex
2F (
) 8000hex
210 (
) 10000hex
Since four squared is sixteen, powers of four have an even easier relation:
4x
value
40 1
41 4
42 10hex
43 40hex
44 100hex
45 400hex
46 1000hex
47 4000hex
48 10000hex
This also makes tetration easier when using two and four since:
3
2 = 24 = 10hex,
4
2 = 216 = 10000hex and
5
2 = 265536 = (1 followed by 16384 zeros)hex.
Etymology
The word hexadecimal is composed of hexa-, derived from the Greek έξ (hex) for "six", and
-decimal, derived from the Latin for "tenth". Webster's Third New International online derives
"hexadecimal" as an alteration of the all-Latin "sexadecimal" (which appears in the earlier Bendix
documentation). The earliest date attested for "hexadecimal" in Merriam-Webster Collegiate
online is 1954, placing it safely in the category of international scientific vocabulary (ISV). It is
common in ISV to mix Greek and Latin combining forms freely. The word "sexagesimal" (for base
60) retains the Latin prefix. Donald Knuth has pointed out that the etymologically correct term is
"senidenary", from the Latin term for "grouped by 16". (The terms "binary", "ternary" and
"quaternary" are from the same Latin construction, and the etymologically correct term for
"decimal" arithmetic is "denary".)[8] Schwartzman notes that the expected form from usual Latin
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phrasing would be "sexadecimal", but computer hackers would be tempted to shorten that word
to "sex".[9] The etymologically proper Greek term would be hexadecadic (although in Modern
Greek deca-hexadic (δεκαεξαδικός) is more commonly used).
Common patterns and humor
For more details on this topic, see Hexspeak.
Hexadecimal is sometimes used in programmer jokes because certain words can be formed using
only hexadecimal digits. Some of these words are "dead", "beef", "babe", and with appropriate
substitutions "c0ffee". Since these are quickly recognizable by programmers, debugging setups
sometimes initialize memory to them to help programmers see when something has not been
initialized. Some people add an H after a number if they want to show that it is written in
hexadecimal. In older Intel assembly syntax, this is sometimes the case.
An example is the magic number in Universal Mach-O files and java class file structure, which is
"CAFEBABE". Single-architecture 32-bit big-endian Mach-O files have the magic number
"FEEDFACE" at their beginning. "DEADBEEF" is sometimes put into uninitialized memory. Microsoft
Windows XP clears its locked index.dat files with the hex codes: "0BADF00D". The Visual C++
remote debugger uses "BADCAB1E" to denote a broken link to the target system.
Two common bit patterns often employed to test hardware are 01010101 and 10101010 (their
corresponding hex values are 55h and AAh, respectively). The reason for their use is to alternate
between off ('0') to on ('1') or vice versa when switching between these two patterns. These two
values are often used together as signatures in critical PC system sectors (e.g., the hex word,
0xAA55 which on little-endian systems is 55h followed by AAh, must be at the end of a valid
Master Boot Record).
The following table shows a joke in hexadecimal:
3x12=36
2x12=24
1x12=12
0x12=18
The first three are interpreted as multiplication, but in the last, "0x" signals Hexadecimal
interpretation of 12, which is 18.
Another joke based on the use of a word containing only letters from the first six in the alphabet
(and thus those used in hexadecimal) is...
If only dead people understand hexadecimal, how many people understand hexadecimal?
In this case, "dead" refers to a hexadecimal number DEAD (57005 base 10), as opposed to the
state of not being alive.
A Knuth reward check is one hexadecimal dollar, or $2.56.
Primary numeral system
Similar to dozenal advocacy, there have been occasional attempts to promote hexadecimal as the
preferred numeral system. These attempts usually propose pronunciation and/or symbology.[10]
Sometimes the proposal unifies standard measures so that they are multiples of 16.[11][12][13]
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Hexadecimal - Wikipedia, the free encyclopedia
file:///E:/教程4/￥计算机导论/参考资料/Hexidecimal十...
An example of unifying standard measures is Hexadecimal time which subdivides a day by 16 so
that there are 16 "hexhours" in a day.[13]
Simple key for notations used in article:
Full Text Notation Abbreviation Number Base
binary
bin
2
octal
oct
8
decimal
dec
10
hexadecimal
hex
16
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Hexspeak
HTML
Nibble — one hexadecimal digit can
exactly represent one "nibble"
Numeral system — a list of other base
systems
Web colours
Base32 (content encoding scheme)
Base64 (content encoding scheme)
Binary numeral system
Hex editor
Hexdump
Hexadecimal time
1. ^ "Hexadecimal web colors explained"
(http://www.web-colors-explained.com/hex.php)
. http://www.web-colors-explained.com
/hex.php .
2. ^ Some of C's syntactic descendants are C++,
C#, Java, JavaScript, and Windows
PowerShell
3. ^ The string "\x1B[0m\x1B[25;1H"
specifies the character sequence Esc [ 0 m
Esc [ 2 5 ; 1 H Nul. These are the
escape sequences used on an ANSI terminal
that reset the character set and color, and then
move the cursor to line 25.
4. ^ [http://www.atarimagazines.com/compute
/issue56/107_1_MSX_IS_COMING.php
Compute!, issue 56, January 1985, p. 52
5. ^ BBC BASIC programs are not fully portable
to Microsoft BASIC (without modification)
since the latter takes & to prefix octal values.
(Microsoft BASIC primarily uses &O to prefix
octal, and it uses &H to prefix hexadecimal, but
the ampersand alone yields a default
interpretation as an octal prefix.
6. ^ Donald E. Knuth. The TeXbook (Computers
and Typesetting, Volume A). Reading,
Massachusetts: Addison-Wesley, 1984. ISBN
7.
8.
9.
10.
11.
12.
0-201-13448-9. The source code of the book in
TeX (http://www.ctan.org/tex-archive/systems
/knuth/tex/texbook.tex)
(and a required set
of macros CTAN.org (ftp://tug.ctan.org
/pub/tex-archive/systems/knuth/lib/manmac.tex)
) is available online on CTAN.
^ Letters to the editor: On binary notation,
Bruce A. Martin, Associated Universities Inc.,
Communications of the ACM, Volume 11,
Issue 10 (October 1968) Page: 658
doi:10.1145/364096.364107 (http://dx.doi.org
/10.1145%2F364096.364107)
^ Knuth, Donald. (1969). Donald Knuth, in The
Art of Computer Programming, Volume 2.
ISBN 0-201-03802-1. (Chapter 17.)
^ Schwartzman, S. (1994). The Words of
Mathematics: an etymological dictionary of
mathematical terms used in English. ISBN
0-88385-511-9.
^ "Base 4^2 Hexadecimal Symbol Proposal"
(http://www.hauptmech.com/base42)
.
http://www.hauptmech.com/base42 .
^ "Intuitor Hex Headquarters"
(http://www.intuitor.com/hex/)
.
http://www.intuitor.com/hex/ .
^ "A proposal for addition of the six
Hexadecimal digits (A-F) to Unicode"
2013-11-15 22:53
Hexadecimal - Wikipedia, the free encyclopedia
(http://std.dkuug.dk/jtc1/sc2/wg2/docs/n2677)
. http://std.dkuug.dk/jtc1/sc2/wg2/docs
/n2677 .
13. ^ a b Nystrom, John William (1862). Project of
a New System of Arithmetic, Weight, Measure
file:///E:/教程4/￥计算机导论/参考资料/Hexidecimal十...
and Coins: Proposed to be called the Tonal
System, with Sixteen to the Base
(http://books.google.com
/books?id=aNYGAAAAYAAJ)
.
Philadelphia. http://books.google.com
/books?id=aNYGAAAAYAAJ
.
Retrieved from "http://en.wikipedia.org/wiki/Hexadecimal"
Categories: Computer arithmetic | Positional numeral systems
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